On the equation \(a{f^n} + b (f')^m \equiv 1\). (English) Zbl 1449.30046
Summary: Let \(n, m\) be two positive integers. Some previous researchers proved the existence of meromorphic solutions for the Fermat-type functional equation \({f^n} + (f')^m \equiv 1\) in 2013. This paper extends their results and obtains all general solutions of \(a{f^n} + b (f')^m \equiv 1\).
MSC:
| 30D05 | Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable |
| 34M05 | Entire and meromorphic solutions to ordinary differential equations in the complex domain |
